Traveling waves for a diffusive SIR model with delay and nonlinear incidence

Volume 11, Issue 12, pp 1313--1330 http://dx.doi.org/10.22436/jnsa.011.12.03

Publication Date: September 13, 2018 Submission Date: December 12, 2017 Revision Date: August 04, 2018 Accteptance Date: August 23, 2018

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Authors

Yanmei Wang - School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China. - School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, Shanxi 030006, China. Guirong Liu - School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China. Aimin Zhao - School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China.

Abstract

This paper is concerned with the existence and non-existence of traveling wave solutions for a diffusive SIR model with delay and nonlinear incidence. First, we construct a pair of upper and lower solutions and a bounded cone. Then we prove the existence of traveling wave by using Schauder's fixed point theorem and constructing a suitable Lyapunov functional. The nonexistence of traveling wave is obtained by two-sided Laplace transform. Moreover, numerical simulations support the theoretical results. Finally, we also obtain that the minimal wave speed is decreasing with respect to the latent period and increasing with respect to the diffusion rate of infected individuals.

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ISRP Style

Yanmei Wang, Guirong Liu, Aimin Zhao, Traveling waves for a diffusive SIR model with delay and nonlinear incidence, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 12, 1313--1330

AMA Style

Wang Yanmei, Liu Guirong, Zhao Aimin, Traveling waves for a diffusive SIR model with delay and nonlinear incidence. J. Nonlinear Sci. Appl. (2018); 11(12):1313--1330

Chicago/Turabian Style

Wang, Yanmei, Liu, Guirong, Zhao, Aimin. "Traveling waves for a diffusive SIR model with delay and nonlinear incidence." Journal of Nonlinear Sciences and Applications, 11, no. 12 (2018): 1313--1330

Keywords

SIR model
traveling wave
time delay
nonlinear incidence

MSC

35K57
35C07
92D30

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